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Unformatted text preview: it subtends with the formula A = 1 2 r 2 . The radius is measured to be 2 inches with an error . 02 inches and the angle is measured to be 0 . 5 radian with an error . 001 radian. (a) Give an equation of the tangent plane to A = 1 2 r 2 at r = 2 , = 0 . 5. (b) Use the tangent plane to estimate the maximum error in the calculated area. 6. What is the maximum directional derivative of H ( x,y ) = x 2 + y 3 at (3 ,-1)? (OVER) Scores: 1 2 3 4 5 6 7 8 Total 1 Math 20C (Shenk). Quiz 2 p. 2 7. A rectangular box (Figure 3) is to have of volume of 1 cubic foot. What dimensions should it have to minimize the total area of its six sides? (Use calculus.) y x z FIGURE 3 8. Find the critical points of f ( x,y ) = xy + y 2-3 y and use the second-derivative test to classify them....
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